This invention relates to one-way valves used on vacuum storage bags for clothing and other compressible articles. Clothing, pillows, bedding and other compressible articles are often placed in bags which are evacuated to remove the air and compress the articles for compact storage. These bags require a sealable opening to inert articles into and remove articles from the bag, and they require a one-way valve through which air is removed while blocking reentry of air and re-inflation of the bag. Typically a suction device such as the hose form a vacuum cleaner is placed over the valve to suck air from the bag. The suction created from placing the end of a vacuum cleaner nozzle against the pliable bag surface, or against the flat valves fastened to the pliable bag surfaces, is high. The high suction not only makes it hard to reposition the nozzle but it can damage the bag and can suck portions of the garments or articles inside the bag into the valve and damage the garments and articles. Further, the size and suction of vacuum hoses and their nozzles varies enough that some valves do not work well with some nozzles, especially when the valve opening is located within extending walls or flanges covered by caps. There is thus a need for an improved valve which allows a more controlled removal of the air within a vacuum storage bag.